Multiaxial fatigue life prediction of notched specimens based on multidimensional grey Markov theory.

• The stress and strain distribution on the critical plane is studied. • The concept of strain ratio is proposed. • The correlation degree analysis between relevant factors and fatigue life is carried out with gray theory. • A multidimensional gray Markov model is established by combining the advantages of the multidimensional gray GM(1, N) model and Markov theory. It is always a challenge to accurately predict the fatigue life of notched specimens under multiaxial loading, which is a guarantee of structural integrity. Therefore, in this paper, multiple factors affecting fatigue life are considered and a multidimensional grey Markov model is used for fatigue life prediction. Firstly, the plane of maximum shear strain amplitude is determined as the critical plane. Meanwhile, the stress–strain components on the critical plane are extracted, and the relevant parameters affecting the fatigue life are calculated. Secondly, due to the defects of the grey theory itself, the prediction error is larger. Therefore, the grey model is modified with Markov theory to get the grey Markov model. The correlation degree analysis between relevant factors and fatigue life is carried out with grey theory to analyze the degree of influence of different factors on fatigue life. Finally, the grey Markov model is analyzed and verified using experimental data from Q355(D), GH4169 and Al7050 notched specimens and the results show that the grey Markov model can provide an economical and effective method for multiaxial fatigue life prediction. [ABSTRACT FROM AUTHOR]